A227011 -id:A227011 - cp's OEIS frontend

A230201 Numbers k such that sigma(phi(k)) < k.

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 30, 32, 34, 36, 40, 42, 44, 46, 48, 50, 54, 58, 60, 64, 66, 68, 70, 72, 78, 80, 84, 90, 92, 94, 96, 98, 100, 102, 106, 108, 110, 114, 118, 120, 126, 128, 130, 132, 136, 138, 140, 144, 150, 156, 160, 162, 166, 168

Offset: 1

Vladimir Letsko, Oct 11 2013

nonn

All terms are even. However, sigma(phi(k)) may be equal to k for an odd number k if k+2 is a Fermat prime.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000010, A000203, A001229, A018784, A062402, A066694, A227011, A227927, A230203.

Maple
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for n do if sigma(phi(n))
				
```

Select[Range[200], DivisorSigma[1, EulerPhi[#]] < # &] (* T. D. Noe, Oct 14 2013 *)

isok(n) = sigma(eulerphi(n)) < n; \\ Michel Marcus, Oct 12 2013

A230203 Numbers k such that sigma(phi(k)) > k.

Original entry on oeis.org

5, 7, 9, 11, 13, 17, 19, 21, 23, 25, 26, 27, 29, 31, 33, 35, 37, 38, 39, 41, 43, 45, 47, 49, 51, 52, 53, 55, 56, 57, 59, 61, 62, 63, 65, 67, 69, 71, 73, 74, 75, 76, 77, 79, 81, 82, 83, 85, 86, 87, 88, 89, 91, 93, 95, 97, 99, 101, 103, 104, 105, 107, 109, 111, 112, 113, 115, 116, 117, 119

Offset: 1

Vladimir Letsko, Oct 11 2013

nonn

It seems that the odd number k is not in the sequence if and only if k+2 is a Fermat prime (A019434).

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000010 (phi), A000203 (sigma).

Cf. A230201, A001229, A018784, A019434, A066694, A227011, A227927, A062402, A230203, A018784.

for n do if sigma(phi(n))>n then print{n} fi od:

Select[Range[150],DivisorSigma[1,EulerPhi[#]]>#&] (* Harvey P. Dale, Apr 14 2019 *)

is(k) = sigma(eulerphi(k)) > k; \\ Amiram Eldar, Apr 04 2024

A227927 Numbers n such that phi(sigma(k))/sigma(phi(k)) < phi(sigma(n))/sigma(phi(n)) for all k < n and n is the smallest positive integer with this property.

Original entry on oeis.org

1, 2, 36, 144, 576, 3600, 14400, 921600, 1040400, 4161600, 8643600, 34574400, 266342400, 700131600, 2800526400, 179233689600, 202338032400, 809352129600

Offset: 1

Vladimir Letsko, Oct 09 2013

nonn

All known terms excluding a(2) are perfect squares.

			36 is in the sequence because phi(sigma(36))/sigma(phi(36)) = 18/7 and for all k < 36 phi(sigma(k))/sigma(phi(k)) < 18/7.

Cf. A227011, A062401, A062402, A033632, A229238.

s:= n -> numtheory:-phi(numtheory:-sigma(n))/numtheory:-sigma(numtheory:-phi(n)):
  a,na,A[1],sA[1]:=1,1,1,1:
1;for i from 2 do ss:=s(i): if ss>a then na:=na+1:A[na]:=ss:a:=ss:sA[na]:=i:print(sA[na]) fi od:

cp's OEIS Frontend

A230201 Numbers k such that sigma(phi(k)) < k.

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A230203 Numbers k such that sigma(phi(k)) > k.

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Maple

Mathematica

PARI

A227927 Numbers n such that phi(sigma(k))/sigma(phi(k)) < phi(sigma(n))/sigma(phi(n)) for all k < n and n is the smallest positive integer with this property.

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Maple